Mott insulators and the doping-induced Mott transition within DMFT: exact results for the one-band Hubbard model

TL;DR

This paper provides exact analytical results for the Mott insulator phase in the one-band Hubbard model within DMFT, revealing fundamental properties and universal behaviors near the doping-induced Mott transition.

Contribution

It establishes exact results for key physical quantities in the Mott insulator phase, including self-energies and susceptibilities, and analyzes the transition with numerical NRG methods.

Findings

Exact expressions for local charge and magnetic moments.

Universal scaling behavior near the Mott transition.

Non-vanishing Luttinger integral in the Mott insulator.

Abstract

The paramagnetic phase of the one-band Hubbard model is studied at zero-temperature, within the framework of dynamical mean-field theory, and for general particle-hole asymmetry where a doping-induced Mott transition occurs. Our primary focus is the Mott insulator (MI) phase, and our main aim to establish what can be shown exactly about it. To handle the locally doubly-degenerate MI requires two distinct self-energies, which reflect the broken symmetry nature of the phase and together determine the standard single self-energy. Exact results are obtained for the local charge, local magnetic moment and associated spin susceptibilities, the interaction-renormalised levels, and the low-energy behaviour of the self-energy in the MI phase. The metallic phase is also considered briefly, and shown to acquire an emergent particle-hole symmetry as the Mott transition is approached. Throughout the metal, Luttinger's theorem is reflected in the vanishing of the Luttinger integral; for the generic MI by contrast this is shown to be non-vanishing, but again to have a universal magnitude. Numerical results are also obtained using NRG, for the metal/MI phase boundary, the scaling behaviour of the charge as the Mott transition is aproached from the metal, and associated universal scaling of single-particle dynamics as the low-energy Kondo scale vanishes.